Analysis of Axi-Symmetric Extrusion

Abstract

In the present paper, the axi-symmetric extrusion of the Tresca's solid is analysed by means of the semi-inverse method under the Haar-von Karman hypothesis. At first, the stress field is constructed by assuming the distributions of the pressure and the frictional stress on die surface. Then, the velocity distribution in the slip line field is calculated with the boundary conditions of the velocities of the rigid regions. Here, an arbitrary stream line is considered as the die surface, and the stress and the velocity fields obtained above become the solution of the problem of certain peculiar frictional condition, which is different from the given one. Several iterations of this procedure make the difference sufficiently small. From the numerical calculations, the lower and the upper bounds of the extrusion forces are obtained, which are much better than the usual solutions, and the mean extrusion pressures are found to be 10%∼30% larger than those of the plane strain extrusions. Then the strain distributions are compared with the experimental results analysed by the moire and the gridwork methods.